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16.03 - Residue Curves Click here. 50 2

Residue Curve Modeling using Matlab/chap16/residue.m (8:00) (msu.edu)

Residue curves are powerful guides for distillation column design. Residue curves can be generated using bubble temperature calculations as described in the textbook. This screencast describes the strategy to generate a residue map by generating a series of curves and then inferring the location of the separatrices (distillation boundaries).

04.02 The Microscopic View of Entropy Click here. 50 2

Molecular Nature of S: Thermal Entropy (uakron.edu, 20min) We can explain configurational entropy by studying particles in boxes, but only at constant temperature. How does the entropy change if we change the temperature? Why should it change if we change the temperature? The key is to recognize that energy is quantized, as best exemplified in the Einstein Solid model. We learned in Chapter 1 that energy increases when temperature increases. If we have a constant number of particles confined to lattice locations, then the only way for the energy to increase is if some of the molecules are in higher energy states. These "higher energy states" correspond to faster (higher frequency) vibrations that stretch the bonds (Hookean springs) to larger amplitudes. We can count the number of molecules in each energy state similar to the way we counted the number of molecules in boxes. Then we supplement the formula for configurational entropy changes to arrive at the following simple relation for all changes in entropy for ideal gases: ΔS = Cv ln(T2/T1) + R ln(V2/V1). Note that we have related the entropy to changes in state variables. This observation has two significant implications: (1) entropy must also be a state function (2) we can characterize the entropy by specifying any two variables. For example, substituting V = RT/P into the above equation leads to: ΔS = Cp ln(T2/T1) - R ln(P2/P1).

Comprehension Questions:
1. Show the steps required to derive ΔS = Cp ln(T2/T1) - R ln(P2/P1) from ΔS = Cv ln(T2/T1) + R ln(V2/V1).
2. We derived a memorable equation for adiabatic, reversible, ideal gases in Chapter 2. Hopefully, you have memorized it by now! Apply this formula to compute the change in entropy for adiabatic, reversible, ideal gases as they go through any change in temperature and pressure.
3. Make a table enumerating all the possibilities for 3 oscillators with 4 units of energy. 
4. Compute the change in entropy (J/k) for 100 oscillators going from 3 units of energy to 50 units of energy.
5. Compute the change in entropy (J/K) for 100 particles going from 3 boxes to 50 boxes. (This is a review of configurational entropy.)

01.5 Real Fluids and Tabulated Properties Click here. 50 2

Steam quality given temperature and volume (LearnChemE.com, 9min) Steam quality is the fraction of H2O that exists as vapor. Its computation can be accomplished by knowing one of the saturation properties (T or P) and one of the tabulated properties (V,U,H,S). This kind of calculation is sometimes known as the "lever rule" or "inverse lever rule" because the given property acts like the fulcrum on a lever, specifying whether the liquid or vapor property receives the heavier weight. e.g. if the given property is closer to the saturated vapor value, then the vapor value receives a hevierer weight.


Comprehension Questions:
1. Compute the enthalpy (kJ/kg) at 100 C and a quality (q) of  33%.
2. Compute the entropy (kJ/kg-C) at 200 C and a quality of 90%.

01.3 Molecular Nature of Entropy Click here. 48 5

Molecular Nature of Entropy (uakron.edu, 5min) Entropy is often related to chaos or disorder, but it has a specific, mathematical definition in thermodynamics. There is nothing metaphysical about it. This very brief presentation introduces the conceptual basis of how the arrangements of molecules between boxes can be related to the flow of work energy, or lack thereof, depending on how the process is conducted. This conceptual basis is expanded in Section 4.2 to permit quantitative calculations of entropy changes based on molecular configurations.

14.07 Plotting Ternary LLE Data Click here. 48 5

Hints for Generating LLE Envelopes (2:25) (msu.edu)

This screencasts makes several recommendations that help generate LLE phase envelopes most successfully.

10.04 - Multicomponent VLE & Raoult's Law Calculations Click here. 46.6667 3

This example hypothesizes a "pre-quel" to Example 10.1 in the form of a liquid reactor at 20 bars and asks what temperature the reactor must have been in order to result in the flash at 320K and 8 bars if no heat was added. This requires an adiabatic flash calculation. (7min, uakron.edu) The procedure demonstrated here applies the enthalpy pathway of Fig. 2.6c, with Eqn. 2.45 to estimate heats of vaporization. With this approach, you should be able to solve for mass and energy balances of any mixture at any vapor fraction. You should watch the video about Multicomponent VLE for Ideal Solutions before this one (see link above).

Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."

Comprehension Questions
1. Make a spreadsheet like the one in the video. Modify the compositions  to make a binary system like Example 10.2. Can you reproduce the results of Example 10.2?
2. Suppose a reactor was at 380K and 2MPa with a composition of {0.115, 0.335, 0.15, 0.15, 0.25} for {propane, isobutane, nbutane, isopentane, npentane}. What would be the adiabatic T&q of this stream exiting a valve at 8 bars?

11.02 - Calculations with Activity Coefficients Click here. 46.6667 3

This example shows how to quickly generate a Txy diagram in Excel using the Margules Acid-Base (MAB) model and the Excel solver.(14min, uakron.edu) It is a bit of a sneaky trick that sometimes needs good initial guesses, but it is a lot more convenient than solving for each temperature individually by trial and error.

Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."

Comprehension Questions
VLE data at constant pressure are much more relevant to distillation. Generate the Txy diagram for ethanol+benzene using the MAB model (a) at 1 bar (b) at 20 bars. Does the azeotrope change? How might you use these observations to "bust" the azeotrope and obtain pure ethanol and pure benzene? (Hint: use more than one distillation column?)

11.02 - Calculations with Activity Coefficients Click here. 46.6667 3

This example shows how to predict activity coefficients in Excel using the Margules Acid-Base (MAB) model.(8min, uakron.edu) Sometimes you just need a quick estimate of whether to suspect an azeotrope or LLE or some other anomalous behavior. If the MAB model indicates a possible problem, it's time to go to the library or the lab and validate your model with experimental data.

Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."

Comprehension Questions
1. Order the following binary systems from most compatible to least compatible according to the MAB model:
(Note: negative deviations from Raoult's law indicate greater "compatibility," although they may generate azeotropes.)
(a) ethanol+water (b) ethanol+benzene (c) ethanol+diethylamine (d) n-pentane+n-pentanol (e) n-hexane+benzene
2. Pick a couple of binary systems from the Korean Database (Hint: use Internet Explorer for KDB) and compare the experimental data to the MAB predictions. Refine your predicted M1 parameter by calling the solver to minimize the sum of squared deviations between the predicted and experimental pressures. If there was an azeotrope in one of your systems, did the MAB model miss it or was it qualitatively correct?

06.2 Derivative Relations Click here. 46.6667 3

Assembling your derivative toolbox including the triple product rule, (uakron.edu, 13min) Beginning with the fundamental property relation, substitutions lead to Eqns. 6.4-6.7. Differentiating these and equating through exact differentials leads to Eqns. 6.29-6.32 (aka. Maxwell's Relations). Combining Maxwell's Relations with Eqns. 6.4-6.7 leads to Eqns. 6.37-6.41. With these tools in hand, and Eqn. 6.15 (aka. Triple Product Rule), you have all the tools you need to quickly transform any derivative into "expressions involving Cp, Cv, P, V, T, and their derivatives." This capability is fundamental to obtaining expressions for U, H, and S from any given equation of state for any chemical of interest. Four sample derivations are illustrated: (∂U/∂V)T, (∂T/∂S)V, (∂T/∂V)S, (∂S/∂V)A,

Comprehension Questions:

1. Transform the following into "expressions involving Cp, Cv, P, V, T, and their derivatives:" (∂T/∂V)S.

2. Transform the following into "expressions involving Cp, Cv, P, V, T, and their derivatives." Your expression may involve absolute values of S as long as they are not associated with any derivative. (∂T/∂U)P.

07.06 Solving The Cubic EOS for Z Click here. 46.6667 3

Using a macro to create an isotherm (Excel) (msu.edu, 14:31) The tabular Excel display is convenient for viewing all the intermediate values, but no so good for building a table such as for an isotherm. This screencast shows how to write/edit a macro to build a table by copying/pasting values. The screencast creates an isotherm on a Z vs. Pr plot over 0.01 < Pr < 10.

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